GCEFurther MathematicsSets and Binary Operations2020

A binary operation ⊕ is defined on the set of integers by $p \oplus q = p^2 + q^2 - pq$. Find $2 \oplus 3$.

A7CORRECT
B11
C13
D17
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Why the answer is A, and why the others tempt you.
Substituting p = 2 and q = 3: 2 ⊕ 3 = 2² + 3² − (2)(3) = 4 + 9 − 6 = 7. Option B results from computing 4 + 9 − 2 = 11, option C from 4 + 9 = 13 without subtracting pq, and option D from adding pq instead of subtracting.
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